Generalized Heine Identity for Complex Fourier Series of Binomials

In this paper we generalize an identity first given by Heinrich Eduard Heine in his treatise, {\it Handbuch der Kugelfunctionen, Theorie und Anwendungen (1881), which gives a Fourier series for $1/[z-\cos\psi]^{1/2}$, for $z,\psi\in\R$, and $z>1$, in terms of associated Legendre functions of the second kind with odd-half-integer degree and vanishing order. In this paper we give a generalization of this identity as a Fourier series of $1/[z-\cos\psi]^\mu$, where z,\mu\in\C, $|z|>1$, and the coefficients of the expansion are given in terms of the same functions with order given by $\frac12-\mu$. We are also able to compute certain closed-form expressions for associated Legendre functions of the second kind.Comment: 12 page

A Remarkable Identity Involving Bessel Functions

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical examples of the identity are discussed.Comment: 10 pages, 2 figure

Improved analysis of the bounds from the electroweak precision tests on the 4-site model

We present a new complete analysis of the electroweak precision observables within the recently proposed 4-site Higgsless model, which is based on the SU(2)_L x SU(2)_1 x SU(2)_2 x U(1)_Y gauge symmetry and predicts six extra gauge bosons, W_{1,2} and Z_{1,2}. Within the epsilon_i (i=1,2,3,b) parametrization, we compute for the first time the EWPT bounds via a complete numerical algorithm going beyond commonly used approximations. Both epsilon_{1,3} impose strong constraints. Hence, it is mandatory to consider them jointly when extracting EWPT bounds and to fully take in to account the correlations among the electroweak precison measurements. The phenomenological consequence is that the extra gauge bosons must be heavier than 250 GeV. Their couplings to SM fermions, even if bounded, might be of the same order of magnitude than the SM ones. In contrast to other Higgsless models, the 4-site model is not fermiophobic. The new gauge bosons could thus be discovered in the favoured Drell-Yan channel already during the present run of the LHC experiment.Comment: Latex file, 35 pages, 10 figures, corrected typos, published versio

Polynomial solutions of nonlinear integral equations

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.Comment: 10 page

Activation of angiotensin type 2 receptors prevents diabetic complications in female db/db mice by nitric oxide‐mediated mechanisms

Background and Purpose: The AT2 receptor plays a role in metabolism by opposing the actions triggered by the AT1 receptors. Activation of AT2 receptors has been shown to enhance insulin sensitivity in both normal and insulin resistance animal models. In this study, we investigated the mechanism by which AT2 receptors activation improves metabolism in diabetic mice. Experimental Approach: Female diabetic (db/db) and non-diabetic (db/+) mice were treated for 1 month with the selective AT2 agonist, compound 21 (C21, 0.3 mg·kg−1·day−1, s.c.). To evaluate whether the effects of C21 depend on NO production, a subgroup of mice was treated with C21 plus a sub-pressor dose of the NOS inhibitor l-NAME (0.1 mg·ml−1, drinking water). Key Results: C21-treated db/db mice displayed improved glucose and pyruvate tolerance compared with saline-treated db/db mice. Also, C21-treated db/db mice showed reduced liver weight and decreased hepatic lipid accumulation compared with saline-treated db/db mice. Insulin signalling analysis showed increased phosphorylation of the insulin receptor, Akt and FOXO1 in the livers of C21-treated db/db mice compared with saline-treated counterparts. These findings were associated with increased adiponectin levels in plasma and adipose tissue and reduced adipocyte size in inguinal fat. The beneficial effects of AT2 receptors activation were associated with increased eNOS phosphorylation and higher levels of NO metabolites and were abolished by l-NAME. Conclusion and Implications: Chronic C21 infusion exerts beneficial metabolic effects in female diabetic db/db mice, alleviating type 2 diabetes complications, through a mechanism that involves NO production.Fil: Dominici, Fernando Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Veiras, Luciana Cecilia. Cedars Sinai Medical Center; Estados UnidosFil: Shen, Justin Z.Y.. Cedars Sinai Medical Center; Estados UnidosFil: Bernstein, Ellen A.. Cedars Sinai Medical Center; Estados UnidosFil: Quiroga, Diego Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Química y Físico-Química Biológicas "Prof. Alejandro C. Paladini". Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Instituto de Química y Físico-Química Biológicas; ArgentinaFil: Steckelings, Ulrike M.. University of Southern Denmark; DinamarcaFil: Bernstein, Kenneth E.. Cedars Sinai Medical Center; Estados UnidosFil: Giani, Jorge F.. Cedars Sinai Medical Center; Estados Unido

Crowdsourcing hypothesis tests: Making transparent how design choices shape research results

To what extent are research results influenced by subjective decisions that scientists make as they design studies? Fifteen research teams independently designed studies to answer fiveoriginal research questions related to moral judgments, negotiations, and implicit cognition. Participants from two separate large samples (total N > 15,000) were then randomly assigned to complete one version of each study. Effect sizes varied dramatically across different sets of materials designed to test the same hypothesis: materials from different teams renderedstatistically significant effects in opposite directions for four out of five hypotheses, with the narrowest range in estimates being d = -0.37 to +0.26. Meta-analysis and a Bayesian perspective on the results revealed overall support for two hypotheses, and a lack of support for three hypotheses. Overall, practically none of the variability in effect sizes was attributable to the skill of the research team in designing materials, while considerable variability was attributable to the hypothesis being tested. In a forecasting survey, predictions of other scientists were significantly correlated with study results, both across and within hypotheses. Crowdsourced testing of research hypotheses helps reveal the true consistency of empirical support for a scientific claim.</div

Golfo di Taranto (Tavola 9, Fogli 40-46)

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